Chapter 7.5, Problem 3CYU

To determine

To find: The distance between cat and pupil.

Answer to Problem 3CYU

35.71 inches

Explanation of Solution

Given:

  

  $\Delta ABE\sim \Delta DBC$

Cat is 10 inches tall.

Retinal image is 7 mm tall.

Distance from pupil to retina is 25 mm.

  $\Delta ABE\sim \Delta DBC$

In two similar triangles, the ratio of their corresponding sides, altitudes are equal.

Altitude in the $\Delta ABE$ is the distance between cat and pupil.

Let this altitude = $x$ inches

Altitude in the $\Delta DBC$ is the distance between pupil and retina which is equal to 25 mm.

Applying the ratio:

  $\begin{array}{l}\Rightarrow \frac{10}{7}=\frac{x}{25}\\ \Rightarrow x=35.71\end{array}$

The distance between cat and pupil is 35.71 inches.